The limited adaptivity of current robots is preventing their widespread application. However, nowadays there are mature techniques available to palliate this deficiency. After briefly surveying the several levels of adaptivity required and the disciplines addressing each of them, the paper concentrates on the contributions of the field of Neural Networks to improve sensorimotor adaptivity. Since sensorimotor mappings lie at the base of all robot activity, making them adaptable to the robot conditions (e.g., tear-and-wear) and environmental variations greatly widens the range of applications. Several experimental systems are described which rely on the following adaptive mappings: inverse kinematics, inverse dynamics, visuomotor and force-control mappings. Finally, some methodologic and computational issues are discussed.